Semiconductor Physics - IFM

Semiconductor Physics10p PhD Course18 LecturesNov-Dec 2011 and Jan – Feb 2012LiteratureSemiconductor Physics – K. SeegerThe Physics of Semiconductors – GrundmannBasic Semiconductors Physics - HamaguchiElectronic and Optoelectronic Properties of Semiconductors - SinghQuantum Well Wires and Dots – HartmannWave Mechanics Applied to Semiconductor Heterostructures - BastardFundamentals of Semiconductor Physics and Devices – Enderlein & HoringExaminationHomework Problems (6p)Written Exam (4p)AdditionallyYour own research area.Background courses (Solid State Physics, SC Physics, Sc Devices)

Course Layout1. Introduction2. Crystal and Energy Band structure3. Semiconductor Statistics4. Defects and Impurities5. Optical Properties I : Absorption and Reflection6. Optical Properties II : Recombinations7. Carrier Diffusion8. Scattering Processes9. Charge Transport10. Surface Properties11. Low Dimensional Structures12. Heterostructures13. Quantum Wells/Dots14. Organic Semiconductors15. Graphene16. Reserve and Summary

Based on :The Physics of Semiconductors, Grundmann, Chapter 9.Semiconductor Optics, C.F. Klingshirn, Ch. 9-14Lecture Anne Henry, IFMLecture Ivan Ivanov, IFMLecture Micheal Reshchikov,Virgina Commonwelth University,Richmond, USA

Lecture LayoutOptical TechniquesPhotoluminscenceOptical RecombinationsBand-to-BandDAPFree ExcitonBound ExcitonTemperature DependenceInternal TransitionsRecombination ProcessesTime Resolved Photolumnscence

Optical techniquesLUMINESCENCE: spontaneous emission of light in solids Fluorescence: fast luminescence (electric-dipole allowed) Phosphorescence: slow luminescence (electric-dipole forbidden) Photo-luminescence (optical excitation) Cathodo-luminescence (cathode ray (e-beam) excitation) Electro-luminescence (electrical excitation) Thermo-luminescence (heating) Chemo-luminescence (chemical reaction)FTIR Fourier Transform Infrared ReflectivityRAMAN Phonon Scattering

PL : PhotoluminscenceLaserExcitation above bandgap, creates electrons and holes.Cryostat Normally Liquid He, 2 KDetector PMT Photomultipliertube, scanning of monochromatorCCD

FTIR – Fourier Transform Infrared SpectroscopyMichelson InterferometerInterference from fixed and moving mirroris converted by Fourir Transform tointensity spectrumAdvantages:Improved Signal/NoiseImproved resolutionDisadvantagesRequires internal light source to monitormirror movement.Cannot use sensitive detectors in visiblerange.Mainly used for absorption and luminscencein the infrared. λ 1 µm.

RecombinationExcited electronsDDExcitationħνAAARCreated holesBBFBDAPFEBEIBEIT

RecombinationDirectIn-directEnergy and Momentum must be conserved

Band-to-BandSpontaneous recombination rate dependenton electron and hole occupancy in each bandPL Intensity

Free-to-BoundFree-to-Bound (FB)recombinations dominates athigher temperatures, whenDonors and Acceptors areionized.GaNFrom M. ReshchikovVirgina CommonwelyhUniv, Richmond USA

Free-to-Bound : Spectral BroadeningAt higher temperatures carriersare distributed in energy in theconduction band.Involvment of phonons in therecombination.

DAP : Donor-Acceptor-PairsRemote pairsCONDUCTION BANDDARAVALENCE BANDDClose pairsDAR a

DAP : Donor-Acceptor-PairsUnder certain conditions sharp lines related to specific DonorAcceptor pair distance.

DAP : Donor-Acceptor-PairsFrom Ivan Ivanov, IFM

DAP : Donor-Acceptor-PairsIn SiC two different donorand Acceptor positionsHexagonal (h)Cubic (k)Possible DAP arrangments: Dh-Ah (hh set) Dh-Ak (hk set) Dk-Ah (kh set) Dk-Ak (kk set)}equivalentstructure

DAP : Donor-Acceptor-PairsFor deep donors and acceptors –involvment of phonons.For direct bandgapsemiconductors mainly LOphonons.Broadening dependent of numberof involved phonons, N.S : Huang-Rhys factor (averagenumber of involved phonons)

DAP : Donor-Acceptor-PairsHuang Rhys Factor:Dependent on thedisplacement, q, in theconfiguration coordinate(CC) scheme.S 1 Weak couplingNo-phonon linedominates.S 1 Strong couplingBroadening and shifttoeards lower energies.

FE : Free ExcitonsElectron – hole pair.Free to move in the lattice.Requires high purity material, andlow temperatures.Binding energies 5 – 50 meV

BE : Bound Excitons :The mechanism of binding exciton

Bound Excitons : Haynes RulesThe empirical Haynes’ rule: The binding energy of an exciton to a shallow donor (acceptor)is proportional to some degree of the ground-state energy of this donor (acceptor).

Free Excitons : Direct BandgapFE present in high qualitymaterials.No-phonon line dominates.Weak coupling to opticalphonons, LO

Excitons : Fine StructureIn p-type layer relativeintensity between Donor andAcceptor BE changes

Excitons : Fine StructureIn HVP GaNTwo differentDonors.Splitting of valenceband gives threedifferent freeexcitons.XA, XB and XCExcited free excitonstates XAn 2Two-electrontransitions ( )2eElectron-holerecombination leavesremaining electron inexcited state

Excitons : Fine Structure

Bound Excitons : Indirect Bandgap3C3C4H6H6HNPNPPL Intensity (a.u)LA LOLAQ0TOP766.5 1017 cm-3RLOTATAS0P0I76TO1.8 1015 cm-3LANPI76TAP0LOTO2.3 1014 cm-31.5 1015 cm-324002350230022503300 3250 3200 3150 3100 30503000295029002850Photon Energy (meV)SiC:N1 NPSiC:N1 NP phononphononreplicasreplicas2 2NPNP phononphononreplicasreplicas3 3NPNP phononphononreplicasreplicasBE: ħω Eg – EFE – EBE - Ephonon

BE : Local phonon spectrumDI and DII is a common butnot identified defect inSiC:4HDI one defct in as-grownmaterial. Local phononreplicas related to thedefect distortiondependent of defectsymmetri.DII several (?) defects inirradiated material withexcited states and localphon replicas.

Bound Excitons : Relative IntensitiesRelative intensities between freeexciton and bound excitonchanges with donor doping.SiC:4H T 2KNPLAQ0P76TAP06.5 1017 cm-3LOTO1.8 1015 cm-3I762.3 1014 cm-33300 3250 3200 3150 3100 3050Photon Energy (meV)Lower doping gives increased FErecombinationCan be used to determine dopinglevel.

Multiple Bound 3LATAP2NPMultiple Bound Exciton Complexes: Multiple electron-hole pairsbound at neutral donor, seen in Si, GaP, CdSe and SiC

fitspectrumcomposing lines14-315b) 4H-SiC: n 2.3 10cma) 4H-SiC: n 8.1 10IP76.468-3cmI76.4fitspectrum composing linesQ51PQ68513880388438883880Wavelength (Å)38843888Wavelength (Å)1004H-SiCI76.4Q0n 5.2x1014 R (cm-3)R BE/FEPL intensity (arb. units)Bound Excitons : Doping Dependence1010.114101E 1415101E 151617101E 16101E 17-3Net carrier concentration (cm )(CV measurement)

Bound Excitons : Doping DependenceAt higher doping the BE line broadens and shift to lower energies due tobandgap narrowing.PL position used to determine doping.

PL : Temperature Dependence

PL : Temperature Dependence

PL : Temperature DependenceSpectra dominated byBE at lowtemperatures.These ionize and theFE intensity increases.Increased spectralbroadening withtemperature.Red-shift due toreduced bandgap withtemperature.At room-temperaturedifficult to distinguishbetween FE and FB andBB recombinations.

Internal TransitionsTransitions between differentelectronic states of impurities.Mostlt related to deep defects.Excitations seen in absorbtion.Relaxations seen inphotoluminscence.Transitions at relatively lowenergies, as compared tobandgap.

Internal Transitions : V in SiCV, Vanadium substitutional on Si-site[Ar] 3d3 4s2 (5 valence electrons)4 for bonds, 1 remaining 3d1 strongly bound to the impurity.5-fold degnerate (10 including spin) energy levelsspin degeneracy ofthe state (2S 1 2)notation of atomic d-state, n 3,l 2, 2l 1 5-fold degeneracy.In tetrahedral symmetry the state splits in a doubly and triply degeneratestates (disregarding spin).

Internal Transitions : V in SiCWhen the symmetry is reducedto trigonal, further splittingoccurs.Finally, when the spin-orbitinteraction is included.

Internal Transitions : V in SiCSource: Kaufmann & Dörnen, Phys. Rev. B 55, 13009 (1997)

Recombination MechanismsExcited States decays toequilibrium by differentmechanisms RadiativeNon-radiativeAuger RecombinationSurface recombinationTunneling processesThermal IonisationDiffusionThe total decay rate is a sum of allrecombination mechanisms, ww wr wnr ws wt wTh wD BBFBDAPFEBE

TRPL - Time Resolved PLExcitons in direct bandgap materialsRadiative recombinationsExponential decaytimescale nsecExcitons in indirect bandgap materialsNon-radiative Auger recombinationsExponential decaytimescale nsecDAPRadiative recombinationNon-exponential decaytimescale µsecIBERadiative recombinationExponential decaytimescale µsec-msec

TRPL – Temperature DependenceAt higher temperatures whenexciton or donor/acceptor ionize,the decaytime decreases.Additional recombination path forthe recombination.Can be used to determineactivation energies.Example:DAP band in GaN gives donorenergy.Isoelectronic bound exciton givesactivation energies andrecombination times for excitedstates.

Carrier KineticsCarrier relaxation in CB and VBtimescale 1psFaster for LO emission andslower for LA and TA.Capture to Donors and Acceptorstimescale 100ps

PL : Full Spectral RangeGaNFree ExcitonsBound ExcitonsDA-pairsFB

Extended defects:Stacking faults, optical properties

Extended defects: an exampleStacking faults, optical propertiesperiodic crystal potentialperturbation from thestacking faultalways capable of binding one carrier bindingexciton is always possible! (Free, but confined in2D).

Extendeddefects:anexampleStacking faults, optical propertiesOptical signature: Free-exciton-like emission(but at odd energy position)Source: J. Hassan et al., J. Appl. Phys. 105, 123513 2009

The Physics of Semiconductors – Grundmann . Basic Semiconductors Physics - Hamaguchi . Introduction 2. Crystal and Energy Band structure 3. Semiconductor Statistics 4. Defects and Impurities . Lecture Ivan Ivanov, IFM Lecture Micheal Re